Step 1: Place the chicken breasts between two sheets of plastic wrap and pound with a meat mallet to an even 1/2-inch thickness.
Step 2: Place the 1/2 cup flour in one shallow dish. In a second dish, whisk together the eggs and 2 tablespoons of milk. In a third dish, place the crushed pretzels.
Step 3: Season chicken with pepper. Dredge each breast in flour, dip in the egg mixture, and finally coat thoroughly with the crushed pretzels, pressing to adhere.
Step 4: Heat the oil in a large skillet over medium heat. Fry the chicken for about 4-5 minutes per side until the crust is golden brown and the internal temperature reaches 165°F. Remove to a paper-towel-lined plate.
Step 5: In a small saucepan, melt the butter over medium heat. Whisk in the 1 tablespoon of flour and cook for 1 minute. Slowly whisk in the 1/2 cup milk until thickened.
Step 6: Stir in the Dijon mustard and shredded cheddar cheese. Whisk until the cheese is completely melted and the sauce is smooth.
Step 7: Serve the crispy chicken immediately, drizzled with the warm Mustard-Cheddar sauce.